Workspace & Efforts

What is an Effort?

An Effortis the atomic unit of research progress in Mathub. Each effort represents a single mathematical contribution: a theorem proof, a computation, a lemma, a counterexample, or a literature reference. Efforts are collected in a project'sWorkspace and linked together via dependency graphs.

Effort Types and Status

Each effort has a status reflecting its current state:

Creating and Editing Efforts

Step 1: Create a New Effort

Click "New Effort" in the Workspace tab. Give it a title and select a type.

Step 2: Write Your Content

Use the Effort Document editor (Markdown + LaTeX). For example:

## Theorem (Main Result)

Let $f: X \to Y$ be a continuous map between compact Hausdorff spaces.
If $f$ is bijective, then $f$ is a homeomorphism.

**Proof.** Since $X$ is compact and $Y$ is Hausdorff, every closed subset
of $X$ is compact, hence its image under $f$ is compact, hence closed in $Y$.
Therefore $f$ is a closed map, and since it is a continuous bijection,
it is a homeomorphism. $\square$

Step 3: Set Status and Tags

Mark the effort status (DRAFT → PROMISING → VERIFIED) and add relevant tags. Tags can be added manually or suggested by the AI.

Structured Proofs

The Structure tab provides a tree-based proof editor where you can break down a proof into a hierarchy of ProofSteps:

• Step types — Lemma, Claim, Case, Subcase, Remark, Definition
• Status markers — Complete, In Progress, Needs Review, Gap
• Dependencies — Link steps that depend on other steps or efforts

This structured view makes it easy to identify gaps in a proof, track progress, and parallelize work among collaborators.

Review System

Mathub includes a peer review system inspired by GitHub pull request reviews:

Requesting a Review

Click "Request Review" on an effort to ask specific collaborators to review your work.

Submitting a Review

Reviewers can:

• Approve — Mark the effort as verified
• Request Changes — Ask for revisions with specific feedback
• Comment — Leave general feedback without approving or rejecting

Inline Comments

Select any text in the effort document to leave an inline comment with anchor text. This allows precise, line-level feedback on proofs and arguments.

Version History

Every edit to an effort is tracked. The History tab shows all versions with:

• Timestamp and author
• Diff view highlighting additions and deletions
• Ability to restore any previous version

Pull Requests & Branches

For larger changes, create a branch of an effort and submit a Pull Request when ready. This follows the familiar Git workflow:

1. Create a branch from the main effort
2. Make your changes on the branch
3. Open a PR for review
4. Merge after approval

Issues & Milestones

Track open questions and tasks with Issues. Group related issues into Milestones to track progress toward specific research goals.

Tags

Tag efforts with keywords for easy discovery. Tags can be:

• Manual — Added by the author or collaborators
• AI-suggested — The AI Assistant analyzes effort content and suggests relevant tags

Difficulty Estimate

Each effort can include a difficulty estimate to help collaborators gauge the level of expertise and time needed.

Git Integration

Every effort has a Git-backed repository. Clone it locally:

git clone https://mathub.example.com/git/<project-slug>/<effort-slug>.git

Push changes from your local editor and they'll appear in the Mathub workspace.

Dependency Graph

Efforts within a project are linked by logical dependencies. The dependency graph visualizes how efforts relate to each other — which lemmas support which theorems, which computations feed into which results.